The friction characteristics of single-layer h-BN, MoS2, and graphene were systematically investigated via friction force microscopy measurements at various operational (e.g., normal force and sliding speed) and environmental (e.g., relative humidity and thermal annealing) conditions. The low friction characteristics of these single-layer materials were clearly observed from the normal force-dependent friction results, and their interfacial shear strengths were further estimated using a Hertz-plus-offset model. In addition, speed-dependent friction characteristics clearly demonstrated two regimes of friction as a function of sliding speed - the first is the logarithmic increase in friction with sliding speed regime at sliding speeds smaller than the critical speed and the second is the friction plateau regime at sliding speeds greater than the critical speed. Fundamental parameters such as effective shape of the interaction potential and its corrugation amplitude for these single-layer materials were characterized using the thermally-activated Prandtl-Tomlinson model. Moreover, friction of single-layer h-BN, MoS2, and graphene was found to increase with relative humidity and decrease with thermal annealing; these trends were attributed to the diffusion of water molecules to the interface between the single-layer materials and their substrates, which leads to an increase in the puckering effect at the tip-material interface and interaction potential corrugation. The enhanced puckering effect was verified via molecular dynamics simulations. Overall, the findings enable a comprehensive understanding of friction characteristics for several classes of two-dimensional materials, which is important to elucidate the feasibility of using these materials as protective and solid-lubricant coating layers for nanoscale devices.